Impact response of high density flexible polyurethane foam(6)

the foam compression:h _ε

i ¼ðV 0ÀV 1Þ=V 0t rt ,where V 1is the foam speci fic volume at the top of P1wave.The average strain rates h _ε

i ,estimated on the basis of the recorded waveforms are shown in Fig.8as a function of the Hugoniot stress (coordinates are loga-rithmic).It is apparent that the point with s ¼3.2MPa marks a boundary between two modes of the foam impact response.Below this point the foam structure participates in the establish-ment of the shock front form.Beyond the 3.2-MPa stress the foam structure is completely crushed and the shape of the wave front is maintained by the viscosity and the thermal conductivity of the crushed material.While the stress s ¼3.2MPa marks apparently the point beyond which the voids cease to exist in the compressed foam,it is hardly possible to fix the stress of the onset of the foam ’s crush up.Recalling that in the weakest test,PFA test of Table 1,the impact velocity,v 0¼43.5m/s,and the maximum waveform velocity coincide,and that the departure of the corresponding

Hugoniot point from the isothermal compression curve is negli-gibly small,we can conclude that the foam deformation during this test is still reversible.Respectively,the Hugoniot stress in this test,s ¼0.36MPa,may be considered as the stress of the onset of the foam ’s crush up under shock loading.4.3.Dynamic tensile behavior

The experimentally measured value of the velocity pull-back D w pb allows estimating the dynamic tensile (spall)strength s sp of the foam [19]

s sp ¼12

r 0C D w pb

(4)

where r 0¼409kg/m 3is the initial foam density,and C is the slope of the Raleigh line connecting (on the s Àu plane)the unloaded after loading state of the foam with that corresponding to the collision of the two release waves,generated,respectively,at the free surfaces of the foam impactor and the foam sample.The slope C is determined by the compressibility of the foam under negative stress.Since the latter is unknown,the value of the P1wave propagation velocity U 1z 540m =s corresponding to the impact velocity 355m/s (the impact velocity in the spall-oriented experi-ment),was used as the C estimate.This yields for the dynamic tensile strength of the foam s sp z 0:3MPa.The tensile strength of bulk flexible polyurethanes is within 8e 40MPa [20e 22].It is plausible to assume that the tensile strength of the polyurethane foam with some 65-%porosity should not be lower than 2.8MPa.The measured value of the foam dynamic tensile strength,0.3MPa,is tenfold lower.The difference seems to be related to serious damaging of the foam during the compressive part of the loading cycle.

5.Conclusion

A flexible polyurethane foam with initial density r 0¼409kg/m 3was tested in a series of gun-driven planar impact experiments accompanied by VISAR monitoring of the free surface of foam samples.The velocity of symmetrical (foam e foam)impact in these experiments was varied between 43.5and 600m/s.The average compressive strain rate in these experiments ranged from 3.6Â103s À1to 6.2Â105s À1.

The recorded velocity histories made it possible to establish the principal Hugoniot of the foam in a linear form U S ¼U S 0þsu ¼14.8þ1.318u ,where U S is the velocity of propagation of the wave half-height and u is the particle velocity behind the wave front.Such Hugoniot implies that under strong shock loading maximum,the foam compression is V /V 0¼0.241.The velocity of the release (unloading)wave U UL ,determined from the same velocity histories are found to be some 25%higher than the corresponding U S values.The experiments show that under impact with velocity higher than 43m/s (the shock stress s 1¼0.36MPa),the loading of the foam is accompanied by the foam crush up and by an irreversible heating.A reliable assessment of this heating requires,however,more accurate,than available at present,information on the foam Gruneisen parameter.

Based on the rise times of the recorded velocity histories,one can conclude that under impact with velocity higher than 141m/s (s 1z 3:2MPa),the foam is completely crushed and the foam structure ceases to participate in the establishment of the wave-form front.Starting from this point,the structure of the wave front is controlled by the viscosity and thermal conductivity of the bulk foam

material.

Fig.7.Hugoniot of the foam on the s ÀV /V 0plane.The dashed line is the maximum foam compression V /V 0¼(s À1)/s ¼0.241.The insert shows the low pressure Hugoniot data together with the static compression curve of Fig.1

.

Fig.8.The P1wave rise time (from 0.1u 1to 0.9u 1)as a function of the P1amplitude s 1in logarithmic coordinates.The 3.2-MPa point marks the change of the foam response.

E.Zaretsky et al./International Journal of Impact Engineering 39(2012)1e 7

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